Yup, injured animals most often get put to sleep on site if the injury is severe. If it's not life threatening though we will try and keep it around long enough to find a home. You can always take an injured stray animal to the vet, but are you going to pay the bills? The vet is only going to put the animal down too if no one is going to pay for the animals treatment. It's a business, and business is making money. Sad. I could go into my philosophy on it, but then I'd be dubbed a "Communist" or something of the sort.
At the particular shelter I work at, there is an "Injured Animal Fund" which actually gets dissolved into a City account that isn't specifically for the shelter, it most likely pays for the city officials meals and vacations. FYI. Hey, don't curse me, I work for the animals, not the City in question. I've been part-time for over 3 years now with hopes that someday they will hire me on full-time as an Animal Control Officer so the animals have someone on their side, instead of the peoples side, because believe it or not, most people could care less about some little kids best friend. It's pretty pathetic, but after working there for 3 years, I'm pretty sure most people would abandon their kids too if they couldn't speak and tell the authorities on them or make them feel guilty.
Honestly, taking an animal to a shelter is not the best thing for it. It would be more likely to find its way home without human intervention. On the other hand, it sucks for an animal to not find its way home and get run over or poisoned or abused by cruel people. I love people who bring me animals and then curse me for working there. (sarcasm) That happens A LOT.
Finding a "No-kill" shelter is almost impossible unless the animal is under 20 pounds, because "No-kill" shelters never have room, specifically because they never euthanize, and "who wants a shelter mutt?" when you can go spend $300 on a dog bred in someones backyard with their neighbors retarded, but cute,...dog... so very few animals get adopted from "No-kill" shelters. Honestly, if you want to teach your children the miracle of birth by getting your dog or cat pregnant, be ready to teach them the tragedy of death by bringing them to the shelter to show them what happens to the ones that don't find homes because there are already more animals than there are homes for.. or it takes too much effort to sit in the local Wal-Mart parking lot with a 50 cent piece of posterboard stating "Free animals".... Food for thought.
While I'm on the subject, Texas state law is that we hold an animal for 72 business hours before it can be put up for adoption or euthanized. That's 3 days.... unless it's injured.